Question: All of the 3rd grade teachers and students from Covington went on a field trip to an archaeology museum. Tickets were $$8.50$ each for teachers and $$3.50$ each for students, and the group paid $$62.00$ in total. A few weeks later, the same group visited a science museum where the tickets cost $$17.00$ each for teachers and $$10.00$ each for students, and the group paid $$148.00$ in total. Find the number of teachers and students on the field trips.
Answer: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${8.5x+3.5y = 62}$ ${17x+10y = 148}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-17x-7y = -124}$ ${17x+10y = 148}$ Add the top and bottom equations together. $ 3y = 24 $ $ y = \dfrac{24}{3}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $ {8.5x+3.5y = 62}$ to find $x$ ${8.5x + 3.5}{(8)}{= 62}$ $8.5x+28 = 62$ $8.5x = 34$ $x = \dfrac{34}{8.5}$ ${x = 4}$ You can also plug ${y = 8}$ into $ {17x+10y = 148}$ and get the same answer for $x$ ${17x + 10}{(8)}{= 148}$ ${x = 4}$ There were $4$ teachers and $8$ students on the field trips.